sounds like what mine does, although hasnt been doing it lately, same as you mine stops when i apply the brakes, but i had a bakes off and checked everything, only thing i know of that needs doing in the rear is the subframe bushes, and if it is them, then the brake will stop it as it puts a constant srain on it enough to stop it rattling.
so have a look at subframe bushes while you are under there.
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